How do you find the interval where f is concave up and where f is concave down for f(x)=−(2x3)−(3x2)−7x+2?

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Diya Bass · Accepted Answer

Step 1Concavity has to do with the second derivative of a function.A function is concave up for the intervals where d2dx2f(x)&amp;gt;0A function is concave down for the intervals where d2dx2f(x)&amp;lt;0First, let&#039;s solve for the second derivative of the function.The first derivative:f(x)=−2x3−3x2−7x+2ddx(−2x3−3x2−7x+2)=−2(3)x3−3(2)x−7=−6x2−6x−7The second derivative:f′(x)=−6x2−6x−7ddx(−6x2−6x−7)=−6(2)x−6=−12x−6Intervals where f(x) is concave up:−12x−6&amp;gt;0−12x&amp;gt;6x&amp;lt;−12Intervals where f(x) is concave down:−12x−6&amp;lt;0−12x&amp;lt;6x≻12

How do you find the interval where f is concave

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